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Proof step 1 from proof size-append (conclusion)

⊦ (x0 + x1).flashsize = x0.flashsize + x1.flashsize

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ x1. (x + x1).flashsize = x.flashsize + x1.flashsize ⊦ ((a + x) + x1).flashsize = (a + x).flashsize + x1.flashsize

Rule argument

term: x0

Additional information

Used simplifier rules: size-base: ⊦ [].flashsize = 0;%list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic